Between continuous variables: Pearson
Between a binary and a continuous variable: Mann-Whitney
Between binary variables: Chi-square
Response variable = vit D
Explanatory variables = bmi, lat, alt
##
## Call:
## lm(formula = vitD ~ BMI + Lat_zone + Altitude, data = df_vitd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -49.345 -11.249 -1.246 9.575 79.055
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 89.0005791 1.9919664 44.680 <2e-16 ***
## BMI -0.4979969 0.0580553 -8.578 <2e-16 ***
## Lat_zone -2.2804513 0.2414468 -9.445 <2e-16 ***
## Altitude -0.0060733 0.0003938 -15.421 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.68 on 2393 degrees of freedom
## (741 observations deleted due to missingness)
## Multiple R-squared: 0.1239, Adjusted R-squared: 0.1228
## F-statistic: 112.8 on 3 and 2393 DF, p-value: < 2.2e-16
Response variable = vit D
Explanatory variables = lat, alt
##
## Call:
## lm(formula = vitD ~ Lat_zone + Altitude, data = df_vitd)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.838 -11.895 -1.313 10.260 82.772
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 74.7405951 0.9446322 79.12 <2e-16 ***
## Lat_zone -2.2385537 0.2202442 -10.16 <2e-16 ***
## Altitude -0.0058493 0.0003565 -16.41 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.42 on 3135 degrees of freedom
## Multiple R-squared: 0.09496, Adjusted R-squared: 0.09438
## F-statistic: 164.5 on 2 and 3135 DF, p-value: < 2.2e-16
Response variable = mean Vit D
Explanatory variables = Deaths per 100,000, Altitude, Latitude, & Ethnicity
##
## Call:
## lm(formula = mean_vitD ~ Deaths_ht + Alt + Lat + Ethnicity, data = df_mun)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.2290 -3.7819 0.1014 3.3563 17.7267
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 88.9040762 4.0115430 22.162 < 2e-16 ***
## Deaths_ht -0.0654517 0.0284264 -2.302 0.0227 *
## Alt -0.0064036 0.0005495 -11.654 < 2e-16 ***
## Lat -0.8637112 0.1594275 -5.418 2.48e-07 ***
## Ethnicity -0.0303885 0.0383118 -0.793 0.4290
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.539 on 144 degrees of freedom
## Multiple R-squared: 0.5685, Adjusted R-squared: 0.5565
## F-statistic: 47.43 on 4 and 144 DF, p-value: < 2.2e-16
Explanatory variables, together, explain 30% of the variance in Vit D at municipal scale. When controlling for other variables, each variable shows a negative relation with vit D, but only deaths per 100,000, altitude, and latitude are significant. If ethnicity is removed from the model, results are almost the same in terms of coefficients, their signs, and R2.
Response variable = Deaths per 100,000
Explanatory variables = Altitude and Latitude
##
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat, data = df_mun)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.684 -10.062 -1.104 6.567 59.323
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -19.261431 8.301666 -2.320 0.0217 *
## Alt 0.003873 0.001502 2.579 0.0109 *
## Lat 2.038969 0.354502 5.752 5e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16.13 on 146 degrees of freedom
## Multiple R-squared: 0.1922, Adjusted R-squared: 0.1811
## F-statistic: 17.37 on 2 and 146 DF, p-value: 1.712e-07
Response variable = Deaths per 100,000
Explanatory variables = Altitude, Latitude, nmol < 30
##
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat + nmol_30, data = df_mun)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.308 -9.256 -1.324 7.033 56.424
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -14.954767 8.242257 -1.814 0.07168 .
## Alt 0.002704 0.001521 1.778 0.07758 .
## Lat 1.775510 0.358072 4.959 1.96e-06 ***
## nmol_30 88.748859 30.976930 2.865 0.00479 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.75 on 145 degrees of freedom
## Multiple R-squared: 0.2355, Adjusted R-squared: 0.2197
## F-statistic: 14.89 on 3 and 145 DF, p-value: 1.683e-08